A model of a laminar viscous conducting flow, near a dielectric disc in a uniform magnetic field and in the presence of external rotation, is considered, where there is a uniform suction and an axial temperature gradient between the flow and the disc’s surface. It is assumed that the parameters of the suction or the magnetohydrodynamic (MHD) interaction are such that the nonlinear inertial terms, related to the circulation flow, are negligible in the differential equations of the MHD boundary layer on a rotating disc. Analysis of the motion and energy equations, taking the dependence of density on temperature into account, is carried out using the Dorodnitsyn transformation. The exact analytical solution for the boundary layer and heat transfer equations is obtained and analysed, neglecting the viscous and Joule dissipation. The dependence of the flow characteristics in the boundary layer on the rate of suction and the magnetic field induction is studied. It is shown that the direction of the radial flow in the boundary layer on a disc can be changed, not only by variation of the ratio between the angular velocities in the external flow and the boundary layer, but also by changing the ratio of the temperatures in these two flows, as well as by varying the hydrodynamic Prandtl number. The approximate calculation of a three-dimensional flow in a rotating cylinder with a braking disc (or lid) is carried out, demonstrating that a magnetic field slows the circulation velocity in a rotating cylinder.